In this paper we want to describe in detail how the task of numerically solving the flow through a two-stroke engine with moving parts is solved in an efficient way. The mathematical model behind the scenes is illuminated and the used numerical schemes are specified. First, the computation of the convective flux function is carried out by the AUSMDV Riemann solver, which has been proven to be very efficient in comparison to other schemes. Then the introduction of the temperature dependency of the material properties of the fluid has augmented the realistic setting within the compression and expansion of the hot gas within the cylinder. This temperature dependency of the heat capacity causes a change in the equation of state. The gas is not polytropic any more but calorically imperfect. Thus, the use of a relaxation method is necessary in order to retain our Riemann solver. To account for the complex geometry, it was necessary to realize a special mesh treatment. The computational domain can be assembled by different meshes that are connected in a mass conservative way. Furthermore, the piston and crankshaft motion is obtained by very efficient algorithms. In order to speed up the computation of the numerical solution, different strategies have been followed. Adaptive local time-stepping has been implemented in a time consistent manner. Additionally, a dynamic local mesh adaption with hanging knots is used to reach a better resolution in critical areas. A further reduction in computational time has been obtained by the parallelization of the numerical scheme and the mesh routines. To handle this parallelization of the mesh treatment, an extended partitioning for the dynamic load balancing has been implemented. Finally, a simulation of flow through a real-world geometry of an existing two-stroke engine has been performed, the results have been validated with measured pressure data for this engine, and the flow has been qualitatively and quantitatively studied.
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